surface =
Flatten[Table[{{x, y},
    Sin[x + y + RandomReal[{-0.1, 0.1}]] Sin[2 Pi y x]}, {x, 0, 2 Pi,
    2 Pi/24}, {y, 0, 2 Pi, 2 Pi/24}], 1]

intSurface = Interpolation[surface]

Plot3D[intSurface[x, y], {x, 0, 2 Pi}, {y, 0, 2 Pi}]

planeExample =  1/4 + 1/3 x - 2/3 y
Plot3D[{intSurface[x, y], planeExample}, {x, 0, 2 Pi}, {y, 0, 2 Pi},
PlotStyle -> {Red, Green}]

ContourPlot[
intSurface[x, y] == planeExample, {x, 0, 2 Pi}, {y, 0, 2 Pi}]

 Manipulate[
 
  Row[{
    ContourPlot[
     intSurface[x, y] == c + a x - b y, {x, -Pi, Pi}, {y, -Pi, Pi},
     ImageSize -> 300],
    Plot3D[{intSurface[x, y], c + a x - b y}, {x, -Pi, Pi}, {y, -Pi,
      Pi}, PlotStyle -> {Yellow, Red}, Mesh -> None, PlotPoints -> 30,
     ViewPoint -> {0.01, -2.14, 2.62}, ViewVertical -> {0, 0, 1},
    SphericalRegion -> True, ImageSize -> 450]
   }],

{{a, .275, "X-slope"}, -1, 1, Appearance -> "Labeled"},
{{b, .235, "Y-slope"}, -1, 1, Appearance -> "Labeled"},
{{c, .25, "height"}, -2, 2, Appearance -> "Labeled"},

Initialization :>
  (surface =
    Flatten[Table[{{x, y},
       Sin[x + y + RandomReal[{-0.1, 0.1}]] Sin[2 Pi y x]}, {x, -Pi,
       Pi, 2 Pi/24}, {y, -Pi, Pi, 2 Pi/24}], 1];
   intSurface = Interpolation[surface];)]